1D Analysis of harmonically seeded Free-Electron Lasers

The conventional treatment for deriving Free-Electron Laser (FEL) pendulum equations and gain formula assume that the pondermotive potential is provided by the fundamental radiation. While such treatment is valid for FELs during startup from noise, it is feasible to seed the FEL with a harmonic radiation (h>1) via cavity configurations or outcoupling schemes. When the field amplitude of this harmonic part is higher than that of the fundamental wavelength from spontaneous emission, the FEL dynamics is dictated by the presence of the harmonic content. Here we revisit the 1D FEL equations of motion and gain formula to investigate effects on electron beam dynamics and radiation power output when the FEL is seeded by a harmonic.